My betta has torn a large piece of his caudal fin. The torn off piece is not torn off all the way though, and the piece still hangs off. He got stuck under the filter, and it also damaged his dorsal fin, because he was so stuck I had to pull him out.
Now he isn't eating his food and is a little paler, and he his hiding in this one place and just laying there.
Is this from stress?
And will the piece grow back?
If it does, how long will it take?
What should I do?
He is just a baby betta about 7 weeks old

My betta has torn a large piece of his caudal fin. The torn off piece is not torn off all the way though, and the piece still hangs off. He got stuck under the filter, and it also damaged his dorsal fin, because he was so stuck I had to pull him out.
Now he isn't eating his food and is a little paler, and he his hiding in this one place and just laying there.
Is this from stress?
And will the piece grow back?
If it does, how long will it take?
What should I do?
He is just a baby betta about 7 weeks old

Did all of this happen today? He's probably pretty shaken from getting stuck in the filter, so he might be stressed out. I wouldn't worry if he doesn't eat today, he'll probably have his appetite back soon. Fins grow back, but how long it takes depends on your water conditions and the overall health of your betta. If I were you, I'd treat the water with aquarium salt and remove/change/cover the filter so he doesn't get stuck again.

Housing
What size is your tank?- 3 gallons
What temperature is your tank? around 77 fahrenheit
Does your tank have a filter?yes
Does your tank have an air stone or other type of aeration?no
Is your tank heated?yes
What tank mates does your betta fish live with?none

Food
What type of food do you feed your betta fish?aqueon betta food
How often do you feed your betta fish?2-3 times a day

Maintenance
How often do you perform a water change?once a week
What percentage of the water do you change when you perform a water change?100%
What type of additives do you add to the water when you perform a water change?topfin betta water conditioner

Water Parameters:
Have you tested your water? If so, what are the following parameters? no

Symptoms and Treatment
How has your betta fish's appearance changed?Got a rip in caudal fin
How has your betta fish's behavior changed?Hides, paler, eats less
When did you start noticing the symptoms?a few hours ago
Have you started treating your fish? If so, how?Haven't yet
Does your fish have any history of being ill? no
How old is your fish (approximately)?7 1/2 weeks old

It sounds like stress, and yes, their fins can grow back. There are ways that you can manipulate the filter so that he doesn't get his fins caught in it.

HONESTLY, if you are doing 100% water changes then you don't need a filter. The filter is unnecessary if you do not have your tank cycled. Keep his water warm and clean and his fins will regrow, or you can also do aquarium salt treatments.